This month's topics:

MoMath in the New York Times

The Weekend Arts section of the Times for August 30, 2013 carried Helene Stapinski's report on a visit she, her children and two of their cousins made last summer to the Museum of Mathematics ("MoMath," 11 East 26th Street, opened 12/12/2012). The youngsters were initially turned off by the idea of a museum about mathematics. "They should change the name to the Museum That Has Nothing to Do With Math" suggested her 13-year-old. "Then kids might want to go." But misgivings evaporated at the doors to the museum. The children's "pained looks disappeared, and so did they, lost among the 31 colorful exhibits." We get to hear in detail how the children interacted with the museum: the Square Wheeled Trikes ("Look, no hands!"), the Tracks of Galileo ("Dude, we need to make this steeper"), the Funny Face exhibit, the Math Square, and the Human Tree ("When I asked him what it was all about he shrugged and said it was about division and multiplication. But he didn't seem to care one way or the other. He waved his arms wildly and said he felt like a superhero, images of himself sprouting out of his hands and head."). The final verdict: "This is definitely more fun than I thought it would be."

Ms Stapinski went back the next day to interview MoMath's founders, Glen Whitney and Cindy Lawrence. She learned from Whitney that the museum had been much more successful than anticpated: "We thought we'd have 60,000 visitors the first year, total. But we hit that mark in April." She mentioned her son's remark about the name of the museum; in fact research had shown that the word "math" would turn some people away. Lawrence: "But this is who we are. We're not apologizing. We're saying math is cool and we're going to show you it's cool."

Edward Frenkel in the media

Edward Frenkel (Math, UC Berkeley) is becoming the Cédric Villani of American mathematics. Il est partout (minus the spider and the floppy tie).

September 30. A piece in Slate: The perils of Hacking Math: The National Security Agency is undermining fundamental principles of mathematical knowledge, "both by using advances made in secret by mathematicians on their payroll and by intentionally subverting commonly used security protocols by installing 'backdoors' that make these protocols easier to break." He gives the example of codes based on elliptic curves. "[I]t turns out that there are some elliptic curves that ... actually allow for easy decryption; that's an example of a backdoor. It's a nontrivial mathematical problem to generate such curves ... but it can be done. And according to the reports, the NSA has been pushing [the NIST] ... and various vendors to adopt such special elliptic curves since as early as 2006, knowing full well that they were prone to attacks."

October 3. A review in Nature, by Marcus du Sautoy, of his his new book, Love and Math. Du Sautoy likes the book, and especially its presentation of the Langlands program: "Frenkel deftly takes the reader from the beginnings of this mathematical symphony to the far reaches of our current understanding." What is quite unusual is a box at the bottom of the page with an actual mathematical example. Du Sautoy considers solutions to the equation $y^2+y=x^3-x^2$ mod $p$, $p$ a prime. For example, $(x,y)=(6,3)$ is a solution mod $7$. He remarks that of the $49$ possible mod $7$ $(x,y)$ pairs, exactly nine solve the equation, and in general the number of pairs mod $p$ is approximately $p$, with error $a_p$ (so $a_7=2$). "Remarkably," a function due to Eichler allows the computation of $a_p$ from $p$. In the modular form $$q(1-q)^2(1-q^{11})^2(1-q^{2})^2(1-q^{22})^2(1-q^{3})^2(1-q^{33})^2\cdots,$$ after expanding and collecting terms: $$q-2q^2-q^3+2q^4+q^5+2q^6-2q^7-2q^9-2q^{10}+\cdots,$$ one obtains a series in which the coefficient of $q^p$ is exactly $-a_p$. "This is the seed from which the Langlands program grew. It was like uncovering a wormhole connecting opposite ends of the mathematical universe."

October 9. In The Atlantic, "The Nobel Prize in Physics Is Really a Nobel Prize in Math." Frenkel explains how mathematics is not just the handmaiden of the sciences, but is often an integral part of the science itself. "Even among scientists, it is assumed that mathematics plays a secondary role: It is thought of as a toolkit, not the research itself. ... While this is an important mode of operation, mathematics actually plays a much bigger role in science: It enables us to make groundbreaking leaps that we couldn't make otherwise." He mentions Eistein's discovery of general relativity and Higgs' prediction of the existence of a mass-giving boson as examples of the phenomenon: "Experiment is the ultimate judge of a theory, and that's why we do need expensive and sophisticated machines. But the amazing fact is that scientists like Einstein and Higgs have used the most abstract mathematical knowledge to unlock the deepest secrets of the universe."

October 13, New Scientist, interview by Jacob Aron. Some of the same topics as last month's Wall Street Journal piece reviewed here. But when asked, so what's it really like to be a mathematician? Frenkel answers: "You don't discover something beautiful every day. Most of the time, you work on something for weeks or months, only to realize that it doesn't work. But you never give up, you go back and try to analyze the data that you have, and try to see the analogies and connections to try to come up with a new hypothesis. Then you try to test that." What's the ultimate goal of these efforts? "Imagine that somebody gives you a puzzle, but they don't give you the box, just the pieces. You ... try to put them together to create something of value, something beautiful and powerful. You can think of mathematics as the grand project of building this enormous jigsaw puzzle, with different groups of people working on different parts. Then, every once in a while, somebody finds a bridge between two parts, a way to assemble pieces together so that big chunks of the puzzle connect."

October 14. Frenkel's Slate piece is picked up on The Daily Dish, Andrew Sullivan's über-Blog (8,000,000 pageviews a month). "Amid controversy about the NSA's surveillance program, Edward Frenkel urges his fellow mathematicians to consider the political uses --and abuses-- of their work."

Women in science (and in math)

"Can you spot the real outlier?" by Eileen Pollack, appeared in the New York Times Magazine for October 6, 2013. Pollack is currently Director of the MFA Program at Michigan. Her title refers to the iconic photograph of Einstein, Bohr, Planck and 26 other attendees at the 1927 Solvay Conference on Physics, reproduced in a 2-page spread. The "outlier" is Marie Curie, the only woman in the picture, seated between Planck and Lorenz in the first row. Pollack's question: "Almost 90 years later, why does science remain so much of an old boys' club?" Pollack's article is mostly concerned with physics: she was a physics major at Yale, graduating in 1978, but her senior thesis was supervised by a mathematician (Roger Howe, in fact) and math serves throughout as a symbol for all the sciences, especially as they first appear to students in elementary school. The article draws from a wide spectrum of earlier work. Sources include a 2008 report in the AMS Notices on performances in math competitions, which yielded the quote "Only Asians and nerds do math (extracurricularly)" as an explanation for the low participation of many USA-born students in math clubs and teams; and the 2012 Handelsman report which "directly documented gender bias in American faculty members in three scientific fields --physics, chemistry and biology-- at six major research instiutiotns scattered across the country."

What is new are the personal glimpses. Pollack herself, talking about her early love for mathematics and physics, her success in an outstanding undergraduate research project and how nonetheless her low scientific self-regard (she compared herself to Roger Howe and "judged my talents wanting") drove her out of research and into writing. And, in a different context, "The problem is that most girls--and boys--decide they don't like math and science before these subjects reveal their true beauty." Meg Urry, who at the time of her interview was Chair of Physics at Yale, "flabbergasted" to hear from her own female undergraduates about the derision thay had encountered in high school and how even at Yale "the boys in my group don't take anything I say seriously." Roger Howe, who tells her that "It's very unusual for any undergraduate to do an independent project in mathematics. By that measure, I would have to say that what you did was exceptional," but is "taken aback" when she asks him why he never told her. As she puts it, "The most powerful determinant of whether a woman goes on in science might be whether anyone encourages her to go on."